Distance distributions associated with poisson processes of geometric figures
- 1 March 1977
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 14 (1), 195-199
- https://doi.org/10.2307/3213273
Abstract
Consider a process of identically-shaped (but not necessarily equal-sized) figures (e.g. points, clusters of points, lines, spheres) embedded at random in n-dimensional space. A simple technique is derived for finding the distribution of the distance from a fixed point, chosen independently of the process of figures, to the k th nearest figure. The technique also shows that the distribution is independent of the distribution of the orientations of the figures. It is noted that the distribution obtained above (for equal-sized figures) is identical to the distribution of the distance from a fixed figure to the k th nearest of a random process of points.Keywords
This publication has 5 references indexed in Scilit:
- Some properties of line segment processesJournal of Applied Probability, 1976
- Some properties of line segment processesJournal of Applied Probability, 1976
- über Treffzahlwahrscheinlichkeiten im EikörperfeldProbability Theory and Related Fields, 1968
- The spaces in a uniform random suspension of fibresTransactions of the Faraday Society, 1958
- Distribution of Distance to Nth Neighbour in a Population of Randomly Distributed IndividualsEcology, 1956